...and we're on the same cruise March 16, 2008...
lelms,
I take it that you want to be near the port because you're only coming in the day before and want convenience? If you were staying longer and wanted to see LA, I'd recommend you stay in Santa Monica or elsewhere on the West Side, not near the port...
There are only two really good hotels immediately in the vicinity of the port--the Crowne Plaza San Pedro and the Doubletree San Pedro...the other options NEAR, but not immediately near the port are to stay on the other side of the harbor in Long Beach--Hyatt, Westin, Renaissance, Hilton, Courtyard or Coast...
Long Beach puts you a short cavb ride from the pier in Pedro, but has more restaurants and things to see and do convenient to the hotels...the Aquarium, the Queen Mary, Shoreline Village, etc...and it has a free shuttle system around the downtown tourist area...
San Pedro is a more blue-collar industrial town, but extremely convenient to the RCCL pier...The hotels, I believe, will shuttle you to the pier for free (One restaurant recommendation in San Pedro is the Acapulco--right on the waterfront, just a short ways down from the dock) ...
Traffic in LA can be intimidating to the outsider...If you are planning on stayiong awhile and want to visit Hollywood, Universal, Disney, Beverly Hills, the Getty, Venice Boardwalk, Malibu, etc., a rental car is highly recommended...but, if all you are doing is LAX to harbor-area hotel, hotel to ship and ship to LAX, I'd stick with a shuttle LAX to Pedro and Pedro to LAX and use taxis only if you need them locally (say you're stayning in Pedro, but want to go over to Long Beach to poke around and have a really nice dinner at Parker's Lighthouse or other LB eateries...
Good luck...